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Angular limits of the integrals of the Cauchy type

Josef Král, Dagmar Medková (1997)

Czechoslovak Mathematical Journal

Integrals of the Cauchy type extended over the boundary A of a general compact set A in the complex plane are investigated. Necessary and sufficient conditions on A are established guaranteeing the existence of angular limits of these integrals at a fixed z A for all densities satisfying a Hölder-type condition at z .

Another algebraic proof of Weil's reciprocity

Emma Previato (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

The Burchnall-Chaundy-Krichever correspondence which converts meromorphic functions on a curve into differential operators is used to interpret Weil's reciprocity as the calculation of a resultant.

Application of Salagean and Ruscheweyh Operators on Univalent Holomorphic Functions with Finitely many Coefficients

Najafzadeh, Shahram (2010)

Fractional Calculus and Applied Analysis

MSC 2010: 30C45, 30C50The purpose of the present paper is to introduce a new subclass of holomorphic univalent functions with negative and fixed finitely coefficient based on Salagean and Ruscheweyh differential operators. The various results investigated in this paper include coefficient estimates, extreme points and Radii properties.

Applications arithmétiques de l'étude des valeurs aux entiers négatifs des séries de Dirichlet associées à un polynôme

Philippe Cassou-Noguès (1981)

Annales de l'institut Fourier

Nous étudions les fonctions p -adiques associées à des séries du type Z ( P , Q , ξ ) ( s ) = n N r Q ( n ) ξ n P ( n ) - s dans certains cas, où elles admettent un prolongement méromorphe à C avec un nombre fini de pôles et des valeurs aux entiers négatifs algébriques. On retrouve comme cas particulier les fonctions L p -adiques des corps totalement réels et les fonctions Γ -multiples p -adiques.

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